Step 1: Recall the main danger of succinylcholine.
Succinylcholine opens acetylcholine receptors briefly before blocking them, and this triggers potassium to leave muscle cells and enter the blood. In a normal patient this rise is small and harmless, but in certain conditions it becomes large enough to cause dangerous hyperkalaemia and cardiac arrest.
Step 2: Explain tetanus.
Tetanus toxin causes prolonged muscle spasm and effectively immobilises muscle, which leads to extra, or extrajunctional, acetylcholine receptors spreading across the muscle membrane. Succinylcholine acting on this much larger receptor pool causes an exaggerated potassium leak, so it is avoided.
Step 3: Explain closed head injury and stroke.
Succinylcholine causes fasciculations that transiently raise cerebral blood flow and intracranial pressure, which is unsafe in a head injury where pressure may already be high. Stroke, especially with hemiparesis, also causes disuse of the weak muscle and receptor upregulation similar to other denervation states, adding a hyperkalaemia risk on top of the intracranial pressure concern. Both are treated as relative contraindications.
Step 4: Examine hepatic failure.
Succinylcholine is broken down in the plasma by pseudocholinesterase, which is made in the liver. Severe liver failure can lower pseudocholinesterase levels enough to prolong the drug's action, giving a longer than expected paralysis, but this is a dosing and duration issue, not a receptor upregulation or hyperkalaemia risk. It does not carry the same danger as the other three conditions.
Step 5: Put it together.
Tetanus, closed head injury, and stroke all carry a real risk with succinylcholine, either through hyperkalaemia or raised intracranial pressure, so they are contraindications. Hepatic failure only prolongs the drug's effect and is not a true contraindication.
Final Answer:
\[ \boxed{\text{Hepatic failure}} \]